A roller tappet of the pre-cited type is disclosed in the document DE 100 44 732 A1 considered to be generic. The one-piece, shaped sheet metal tappet housing of the proposed roller tappet comprises a tappet skirt which, starting from a front-end tappet bottom, is configured with a semi-spherical contact surface for a tappet push rod through two or four upwards bent sheet metal strips. A drive roller arranged in an end section of the tappet skirt opposite the tappet bottom is rotatably mounted on an axle that is supported in two opposing sheet metal strips. Although this one-piece, shaped sheet metal tappet housing has a high light-weight and cost-saving potential, the structure of such a roller tappet has considerable inherent drawbacks. Among these is the fact that the sheet metal strips forming the tappet skirt have to be connected to one another through additional manufacturing steps after bending in order to guarantee the required shape rigidity and stability of the tappet housing. On the other hand, the introduction of supporting forces of the axle mounting the drive roller into the axle eyes, which are arranged directly in the tappet skirt, is to be seen as a critical factor in so far as, in comparison with a cast component or an extrusion molded component, tappet housings have much thinner walls possess, already in themselves, a comparatively low shape rigidity, so that even at the introduction of low supporting forces, there exists the risk of an impermissibly strong deformation of the tappet skirt with the result that the roller tappet can get jammed in the tappet guide.